Remark

Tag 018I, permanent. Cite it as [Bourbaki, Tag 018I].

Lie Groups and Lie Algebras, chapter VIII, § 12. Chevalley orders

Chevalley orders in $(\mathfrak{g},\mathfrak{h})$ always exist. Indeed, the Chevalley orders are the sets of the form $\mathscr{H}\oplus \sum_{\alpha\in R}\mathbf{Z}X_{\alpha}$ , where $(X_{\alpha})_{\alpha\in R}$ is a Chevalley system in $(\mathfrak{g},\mathfrak{h})$ and $\mathscr{H}$ is a lattice in $\mathfrak{h}$ such that

Q(R^{\vee})\subset \mathscr{H}\subset P(R^{\vee})\oplus \mathfrak{c}

$(\mathfrak{c}$ being the centre of $\mathfrak{g})$ .

Bourbaki sets the proof directly after the statement, and the corpus does not separate them, so what is above is the statement and its proof together.

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